Effort to get us all on the same page (balloon analogy)

[DaveC426913]

In the balloon analogy I use, galaxies are represented by pennies glued to the balloon. You can see that the pennies do not grow as the balloon's expansion pulls adjacent galaxies apart. Problem solved.

The pennies addition has one other bonus thing in the process.

Whenever discussing the expansion of universe, the very next question is almost inevitably asked is: so is the Earth is getting farther from the Sun, and are atoms are spreading out in our bodies?

Using pennies glued to a balloon, we see that the pennies obviously don't get ripped apart. We know a penny's cohesion can easily overcome any expansive force by the glue. So now it is intuitively obvious why the gravitational cohesion of a galaxy, solar system, or atomic object easily overcomes any expansive force of the universe. Like the glue, the expansive is simply far too weak.

Oops. I see the pennies feature has been introduced here weeks ago.

 

[Lost in Space]

In the balloon analogy I use, galaxies are represented by pennies glued to the balloon. You can see that the pennies do not grow as the balloon's expansion pulls adjacent galaxies apart. Problem solved.

The pennies addition has one other bonus thing in the process.

Whenever discussing the expansion of universe, the very next question is almost inevitably asked is: so is the Earth is getting farther from the Sun, and are atoms are spreading out in our bodies?

Using pennies glued to a balloon, we see that the pennies obviously don't get ripped apart. We know a penny's cohesion can easily overcome any expansive force by the glue. So now it is intuitively obvious why the gravitational cohesion of a galaxy, solar system, or atomic object easily overcomes any expansive force of the universe. Like the glue, the expansive is simply far too weak.

The pennies analogy is a good one, although using this analogy, surely the galaxies would have been much closer together and more gravitationally tied to each other in the past as well as being effectively larger in comparison to the total volume of space? Shouldn't they now be more closer together than they are?

 

[Lost in Space]

The balloon surface is 2D. You have to envision the entire universe as the 3D surface of the balloon. In 3D, no matter what direction you point you can't get off the surface of the balloon. Also consider the inside of the balloon as the past, and the outside of the balloon as the future. so the balloon actually is expanding into something; the future. There may be other balloons, they may bump into each other. But that's another theory.

If the universe is expanding into the future doesn't this imply that the future already exists?

 

[DaveC426913]

The pennies analogy is a good one, although using this analogy, surely the galaxies would have been much closer together and more gravitationally tied to each other in the past as well as being effectively larger in comparison to the total volume of space? Shouldn't they now be more closer together than they are?

Any analogy only goes so far. This is an analogy in qualities, not in quantities. It demonstrates the principle, not the execution.

 

[Lost in Space]

Any analogy only goes so far. This is an analogy in qualities, not in quantities. It demonstrates the principle, not the execution.

Yes, I appreciate the limitations of analogy. So does this mean that the expansion energy of space must have been much greater in the past than the gravity binding the galaxies together, even though they were a lot closer to each other? I've discussed this before on other threads because of local effects such as superclusters and galactic collision. Does it mean that the expansion is not uniform, and could it have something to do with the uneven distribution of mass in the early universe?

 

[RayYates]

...Does it mean that the expansion is not uniform, and could it have something to do with the uneven distribution of mass in the early universe?

I've wondered that myself and hope someone can clarify that point.

More specifically I have less problem with the notion of Dark Energy than Dark Matter; in that I wonder if the "Dark Matter" binding galaxies together is a space-time effect of the rotation. Like a whirl pool in the cosmic stream keeping the debris together and to an observer, moving too fast.

If this is flat wrong, please tell me how so I can get this picture out of my head.

 

[DaveC426913]

I've wondered that myself and hope someone can clarify that point.

More specifically I have less problem with the notion of Dark Energy than Dark Matter; in that I wonder if the "Dark Matter" binding galaxies together is a space-time effect of the rotation. Like a whirl pool in the cosmic stream keeping the debris together and to an observer, moving too fast.

If this is flat wrong, please tell me how so I can get this picture out of my head.

There are several independent sources of evidence of Dark Matter. Some have nothing to do with rotating galaxies. Look up the Bullet Cluster.

 

[Farahday]

On the expanding balloon there is a point within a finite distance from any given origin at which motion in any direction will not increase the distance between the two points. Are you saying this is the case with the "expanding Universe"?

 

[RayYates]

There are several independent sources of evidence of Dark Matter. Some have nothing to do with rotating galaxies. Look up the Bullet Cluster.

Thanks. Fascinating reading.

 

[Lost in Space]

On the expanding balloon there is a point within a finite distance from any given origin at which motion in any direction will not increase the distance between the two points. Are you saying this is the case with the "expanding Universe"?

A balloon can only expand so far before it bursts as its composition is finite. It's an interesting thought however, that some claim the universe can seemingly expand forever. If so spacetime has a beginning but no apparent end therefore it might or might not say something about the infinite. It's hard to imagine that in the very distant future after protons and quarks have decayed whether anything will be left to define the passing of time as we now understand it. According to quantum theory any form of matter left including strings would be unable to completely stop vibrating so the universe will never reach a temperature of absolute zero. But then again what about leakage of energy due to quantum effects? If the vacuum is caused by quantum fluctuations would these define the passing of time alone or would vibrating strings that still survive define the passing of time even if they were dispersed by cosmic distances?

 

[DaveC426913]

On the expanding balloon there is a point within a finite distance from any given origin at which motion in any direction will not increase the distance between the two points.

What point is that?

Are you saying this is the case with the "expanding Universe"?

Not until I grant your assertion above.

[ Aside ]
I may be misunderstanding, but if I take your question literally, there are an infinite number of points that meet your criteria.

Here's what you wrote:

... there is a point within a finite distance from any given origin at which motion in any direction will not increase the distance between the two points.

So: point B - which is one light year distant from point A - is completely free to move anywhere on a sphere one light year in radius from point A. i.e. Motion of B in any direction does not increase the distance between A and B. that meets your criteria. An infinite number of points do.

Since this is a trivial case, I assume it's not what you meant. So what did you mean?
[/ Aside ]

 

[RayYates]

If increasing gravity slows time then time inside galaxies is slower than time between galaxies. If this assumption is correct, how would it affect red shift used to calculate the recession of galaxies?

 

[marcus]

If increasing gravity slows time then time inside galaxies is slower than time between galaxies. If this assumption is correct, how would it affect red shift used to calculate the recession of galaxies?

Hi Ray, you and Dave have been having a good Q/A conversation (good concise Q's and A's) so I'm reluctant to jump in. Maybe Dave will confirm my rough estimate that the grav. redshift effect would typically be so slight as to be lost in the noise. You can look up "grav. redshift" on Wkpd and do the numbers.

The effect was only measured in the radiation from a star sometime in 1955-65. It is so faint it is very hard to detect.

And it is proportional to M/R the mass divided by the distance from center where the photon is emitted. If it is emitted farther from center the effect is less.

The mass of a galaxy might be 10¹¹ times the mass of a star. But a typical light source in the galaxy could be at a distance of 10,000 lightyears from center which is about 10¹¹ times the radius of a star.

So a photon emitted from a star at a moderate distance from center will suffer a grav. redshift from the galaxy gravity which is roughly the same size as what it suffers from the star itself.

And that effect (of the star's gravity) is so tiny that it took sophisticated technique to measure. It was a standing challenge for many years, finally overcome around 1960.

Practically speaking that slight effect would be all smeared out because spectral lines are fuzzy and the light from a galaxy comes from billions of stars at all different distances from center and contributing random motion doppler effects and so on.

In the CMB, the grav redshift (socalled Sachs-Wolfe effect) is about 10^-5 or one thousandth of one percent. This is a rare case where fortunate circumstances allow it to be measured. It is interesting, but it doesn't compete in size with the cosmological redshift which for a typical galaxy is several hundred percent. In other words, recession effect overwhelms gravity effect.

 

[Lost in Space]

In the CMB, the grav redshift (socalled Sachs-Wolfe effect) is about 10^-5 or one thousandth of one percent. This is a rare case where fortunate circumstances allow it to be measured. It is interesting, but it doesn't compete in size with the cosmological redshift which for a typical galaxy is several hundred percent. In other words, recession effect overwhelms gravity effect.

If increased redshift is due to greater distance and gravity is of little consequence as you seem to be sayng, is this also true of the redshift of two comparable galaxies of the same distance in which one has been Einstein lensed? In other words will the lensed galaxy be more redshifted than the one that isn't or will there be no difference and if there was a difference would it be dependent on the strength of the gravity field of the lensing object? Would the distance of the source subject be significant? If there is a difference would it be more noticeable with a similar example being observed at a greater distance as the redshift increases?

Just wondered as spacetime is curved due to the intervening lensing object whether a black hole or galaxy etc. I would have thought that the lensing objects would affect time within their influence and the light from the source object would have to travel further as well. Surely if the light has to travel further, won't it be more redshifted?

 

[marcus]

Hi LiS, the conventional formula for the cosmological redshift has it depend on the proportion that distances have increased during the time the light was in transit.

z + 1 = a(now)/a(then)

a(t) is the scale factor. Most basic function in cosmology. It is what theFriedman equation tells you about.

a(now)/a(then) = 3 would mean that largescale distances were now 3X what they were when the light was emitted and set out on its journey to us.

And then z + 1 = 3 so we would say that z = 2.

So if two bunches of light arrive today, having traveled across open space to us from distant places, then the one that has traveled longest time will be the most redshifted.

Simply because distances will have expanded more while it was in transit for the longer time.

But the lensing you talk about only has a very slight effect on the total path and on the travel time, as a rule. I don't imagine it would make much of a difference.

Still the principle you suggest holds, I think. Bent path means longer travel time. Longer transit time means more time for distances to expand. More expansion means more redshift.

I just came across an interesting paper on dimensionless cosmology. Don't know where to park the link so I'll leave it here for the time being:
http://arxiv.org/abs/1109.0492
Popular account of possible varying alpha constant:
http://astronomy.swin.edu.au/~mmurphy/res.html
Technical paper about it in Physical Review Letters
http://arxiv.org/abs/1008.3907
Douglas Scott (UBC Vancouver) looks like someone to watch on this one.

 

[Mathbrain]

I have read the entire post, and I still have some questions:

1 - Given two galaxy clusters A and B that lie on a line L at time T, where A and B are moving perpendiculr to L as time goes by. At some future time F, we can draw a diagon line D from A at T to B at F. If D is a constant distance, light from A at T will reach B at F. If we can predict the location of B at F, then we can calculate D. My question is given that A and B are moving perpendicular to L at a predictible rate, can we predict D, or will the distance D change by some variables?

2 - Are all instances of CMB from the Big Bang? If so, how is it that we can constantly sense CMB? They would need to be moving at different speeds, or bouncing off something.

WRT baloon analogy.
I think that readers of this forum should be aware that the 2D skin of the baloon is meant to represent a 3D space. Furthermore the baloon analogy is incapable of showing the curvature of space, as an extra dimension is require to express curvature in a geometric manner. That is you can't show 2D space being curved in a 2D space, only a 2D representation of 3D space. I think readers should also be informed that a dimension needs to be perpendicular to all other dimensions, and that a dimension is not an alternate reality.

I'm not saying that the baloon analogy is flawed, I'm just saying that it's limitations should be expressed. Thanks for your post you've help answer a lot of my questions.

 

[marcus]

Periodically I try a new way of explaining expansion to myself (and anybody else for whom the explanation works.) Here is the current explanation.

We are talking about a pattern of expanding distances between observers who are stationary relative to the ancient light that fills the universe.

Barring minor differences in their gravitational potential these observers all perceive time the same way---universe time. They can synchronize their clocks, agree on the age of the universe, agree on the average temperature of the ancient light, and so on. The reason they can do all that is because they are stationary---in effect at rest relative to the original hot gas that filled space before it began to coalesce and fall together. This uniformly distributed matter is a kind of landmark. Or rather its GLOW, the relic light it emitted, is a landmark.
One can be at rest relative to that ancient matter, or its light.

A shared criterion of rest is what allows a shared idea of time, and allows us to talk about distances between observers at a particular moment in time. These are called proper distances and they are what you would measure by any conventional means if you could freeze expansion at that moment (to give yourself time to measure without the distance changing.)

So I would say let's try not to say "expanding universe" or "expanding space" too much because it may engrave the wrong idea on people's brains What we are talking about it a pattern of expanding distances between stationary observers.

The current percentage rate is 1/140 % per million years. This is barely noticeable unless the distance we are talking about is very very large.

In this uniform pattern of expansion, nobody gets anywhere---it does not bring anybody closer to some imagined destination. It doesn't correspond with anything like usual motion. The usual ideas about energy-of-motion and speed limits etc etc do not apply to it.

Notice that the scheme is approximate because the ancient light is not perfectly uniform and the idea of being at rest is only approximate (up to about 1/1000 of a percent.) There is a slight 1/1000 of a percent variation in the temperature of the CMB that can't be gotten rid of, so the idea of being at rest is not perfectly precise.

If anybody reads this and finds things that they think are wrong or that don't work, or other things good or bad to remark on, comments are welcome.

I'm trying to get away from the analogy of space as a "material". The balloon analogy is not meant to suggest that space is a material, it is a way of showing geometric relationships among the galaxies and the photons. There is no rubber. There is only the expanding geometry, a web of real (and imagined what-if) measurements.

Also in response to one of the other posters, curvature does not require an extra dimension. Gauss back in 1820 and Riemann back in 1850 got that all settled Curvature can be experienced intrinsically. There does not have to be an inside or outside of the balloon in order for 2D creatures living in the balloon surface to experience and measure the curvature of their world. It has been almost 300 years now since Carl Gauss realized that.

 

[Mathbrain]

My point wasn't that you need an extra dimension for curvature to exist, I was saying that you need an extra dimension to represent curvature. It isn't enough to say "space is curved". Is it spaced by the inverse square law, as an exponential function, or what?

I am still waiting for my question to be answered.

 

[marcus]

I am still waiting for my question to be answered.

I started a special "Mathbrain questions" thread to respond. Please check it out and, if you have further questions or more to say, continue this discussion there:
https://www.physicsforums.com/showthread.php?t=554838

 

[derek101]

If the balloon analogy is a good analogy,I have a question,because the galaxies are expanding away from each other,what is the fastest galaxy that we know to be traveling away from us,and how far can we see around to the other side of the balloon?

 

[marcus]

If the balloon analogy is a good analogy,I have a question,because the galaxies are expanding away from each other,what is the fastest galaxy that we know to be traveling away from us,and how far can we see around to the other side of the balloon?

I like your question, except I think it's a bad idea to talk of galaxies "traveling away from us", or to think of them as doing that.
In a uniform pattern of distance expansion nobody is traveling in the usual sense because nobody gets anywhere.

It is not motion. It is a change in geometry.

That's a big reason WHY the balloon analogy has generally been helpful to the people who have actually gone and looked at the short movie. Google "wright balloon model"

The thing it does is it shows each galaxy staying fixed at the same latitude longitude place, while photons of light actually travel between and among them. The photons of light always travel at the same speed. You can check that by watching the movie.

And yet a photon of light even though you can see it traveling always at the same speed, does not necessarily get to its destination at that rate. The distance between it and where it is going can actually increase for a while (until the expansion rate slows).

It is a helpful model because you can learn a lot by watching carefully and you can learn a lot which SOUNDS paradoxical when said in words but is actually quite reasonable.

So I hope you have watched that movie or will do so before you start discussing the balloon analogy here.
======================

In direct answer to your questions. We can see the light from matter that is NOW 45.5 billion LY from us. It didn't use to be so far away when it emitted the light which we are not getting from it. But NOW the matter we are looking at, the farthest, is 45.5 billion LY from here, so that is how far we can see.
I am using the definition of distance called proper distance which means what you would measure by conventional means like radar or a long string, if you could just stop the expansion process NOW to give yourself time to measure.

The latest NASA estimate of the circumference of the U, the MINIMUM circumf that it could be now, if it is finite at all, is about 600 billion LY. (Again proper distance)

You asked how far we can see and is that around to the other side and the answer is no it is not around to the other side, the 45 is only a little ways compared with the 600.
And the 600 is only a minimum, a lower bound estimate. It might be much bigger. They did not give any estimate of upper bound.

You asked what rate the distance to the most distant galaxy (so far) is increasing. I believe it is about 2.3 times c. we see other more distant stuff, that is receding at 3 times c. But that stuff has not cooled and condensed into galaxies yet. If you have further questions I hope you will start a thread and ask them. The most distant galaxy is, I believe, UDFj-39546284
If you google it you find that the estimated redshift is 10.3.

Then follow the "morgans" link in my sig to morgan's calculator. Or simply google "cosmos calculator".
Put in the 3 standard parameters (.27 for matter, .73 for cosmo constant, 71 for Hubble rate) and then put in 10.3 and press calculate. It will tell you the current distance and the current rate that distance is increasing which is 2.3c.

 

[megacal]

Hi Marcus, et al =)

I have a Microbiology background, and only have undergraduate math & physics understanding, but am intrigued by cosmology.

I'm sorry I haven't had time yet to go through all the posts in this thread to catch up, but
did see the Balloon Analogy simulation. I get it, and don't have a problem with it.

Can someone please tell me:

1) Do we see the same density of galaxies (eg the Deep Field) regardless where we look?
(edited to reflect previous post...i.e. that we can only see 45 LY across the estimated 600 LY
of the Universe if it's finite).

2) According to Greg Bernhardt in this https://www.physicsforums.com/showthread.php?t=506991 for this forum:

Therefore the best evidence is that the Big Bang happened uniformly, everywhere at once.
Since realistic cosmological models are homogeneous, every point in space has the same properties as every other point, and therefore the models don't have a center.

That appears to be illogical, imho...IF the BB started at an infintesimally small point, it would
by definition have to have a center i.e. point of origin.

3) Prior to the BB (or most recent one), is it possible all the mass was contained in a sphere
the size of e.g. the sun or even the Milky Way vs an infinitely small point?

I can't conceive an infinitely small point containing all the mass of the observable universe
being stabile much less possible. Even though you can mathematically extrapolate backwards to a point, it doesn't necessarily mean that it had to originate from an infinitely small point, but may have from a reasonably large "point".

Also I see it asserted (don't have a ref) that all the matter expanded to the size of the Milky Way in a bazzilionth of a second...waaaay > than C! =O ?

Thanks in advance for the reply!
Cal McGaugh

 

[marcus]

Hi Megacal,

That appears to be illogical, imho...IF the BB started at an infintesimally small point, it would
by definition have to have a center i.e. point of origin.

Think about the balloon analogy. at whatever time the 2d balloon surface is ALL THE SPACE THERE IS AT THAT TIME and all existence is concentrated in that 2d world.

So when the balloon started expanding it was not at a point in today's space.

In our 3D space, by analogy, THERE IS NO POINT OF ORIGIN in today's space.

1) Do we see the same density of galaxies (eg the Deep Field) regardless where we look?
(edited to reflect previous post...i.e. that we can only see 45 LY across the estimated 600 LY
of the Universe if it's finite).

YES. That is approximately right. Roughly the same density profile in every direction of our 3D space. This is the same as what you get with the balloon analogy. think of a 2D creature on the surface.

And density depends also on the redshift or lookback time, because earlier universe was much denser. the density profile is the same in all directions but it also depends on depth how deep in that direction you look.

I can't conceive an infinitely small point containing all the mass of the observable universe
being stabile much less possible.

The classical theory breaks down at the very beginning of expansion. People are working on an improved model that does not develop a singularity. when that is done and tested they will have to try to figure out what matter fields could exist at the start of expansion.

Maybe at some point matter is born out of geometry. Maybe at some very high density matter and geometry are the same quantum thing. we do not have a good theory of how things could have been right at the very start.

People are working hard on this. at least 20 good researchers. This is not what you hear about, like LHC etc etc etc. But the work is going ahead. Inside of 10 years we might have a much better understanding.

I agree if you try to imagine very very high density using ordinary ideas of geometry and matter it does not make sense. Something must be different about this very very high density state. I am resolved to be patient, but I watch the ongoing research in this area with considerable interest.

 

[megacal]

Hi Marcus,

Think about the balloon analogy. at whatever time the 2d balloon surface is ALL THE SPACE THERE IS AT THAT TIME and all existence is concentrated in that 2d world.

So when the balloon started expanding it was not at a point in today's space.

In our 3D space, by analogy, THERE IS NO POINT OF ORIGIN in today's space.

But the balloon and the space inside it is 3D, right? Just because the balloon has expanded doesn't negate the volume. The point of origin still exists (somewhere).

Sorry, but don't understand the model.

 

[DaveC426913]

Hi Marcus,



But the balloon and the space inside it is 3D, right? Just because the balloon has expanded doesn't negate the volume. The point of origin still exists (somewhere).

Sorry, but don't understand the model.

This is where the balloon analogy does not hold. Wwe looka the 2D surfaceof the balloon expanding, and the balloon fills a 3D volume, and we know here its centre is.

But in 3D, it works without there having to be a 4th dimension through which it is expanding.

 

[marcus]

I haven't had time yet to go through all the posts in this thread to catch up, but
did see the Balloon Analogy simulation. I get it,...
...

The thread is very long. I'm glad you watched the short movie. The thread has some useful stuff but it is rather repetitive. Eg we make the point repeatedly that to understand the analogy you have to concentrate. Imagine that 3D space inside and outside the 2D surface does not exist.

All existence is concentrated on the 2D spherical surface.

If any creatures exist they are 2D creatures in that 2D world. They cannot point in any direction not in that world. No point outside it (i.e. inside or outside the balloon) exists for them.

It takes concentration to use the analogy. If you think of the balloon as existing in a surrounding 3D space then it won't work for you as well---you won't "get it."

Hi Marcus,
But the balloon and the space inside it is 3D, right? ...

No. At least that is not the way it has been presented in this thread. Try to think of all existence concentrated on the balloon surface. You are a biologist? Maybe think of the creatures as amoebas slithering in the 2D world between two plates of (miccroscope slide) glass. They can't point their "fingers" or pseudopods in any direction that is not in today's space. No point outside today's 2D space exists for them.

Just as for us there is no point in today's 3D space that is "where expansion began."

How analogies work depends on how you use them. There is no one "right" way to see an analogy so I am just telling you one way to see/use/think about this one.

 

[megacal]

Thanks Marcus & Dave for your replies. I'll concentrate on them, and go through more of this thread and try to grok the concept of a 2D universe, at least until I need some Advil.

The Balloon Analogy isn't as straight forward as I thought looking at the video or
envisioning us as being on or inside the wave front or surface of the balloon.

I just bought a copy of Hawking's illustrated Universe in a Nutshell...it's from 1996, so may be badly out of date, and it doesn't have a ref in the index to the BA, but hope it will give me some understanding of these very mind-bending theories.

In the mean time, I'm going out to the desert tonight to wonder at it all..."My God! It's full of stars!"

Or more accurately..."My God! It's full of galaxies! No, universes!"

 

[megacal]

Hi Marcus,

I've started going through this thread methodically, and am only stumbling over this
part of the BA as you describe how to visualize it mentally:

4. to understand that something can be curved without there being an extra dimension---part of the mental exercise is to picture the balloon surface as all there is, there is no inside the balloon and there is no outside---only the balloon surface exists.
I haven't talked about this part yet.

Ok, no inside or outside...is there the other side? i.e. is the curve continuous
to form a sphere? (balloons are so asymmetrical). Is the surface of the BA convex?
Would a disk would be a better analogy(?)

BTW, looked up the ΛCDM (Wiki), and that was very helpful.

 

[megacal]

Marcus,
came to realize I'm way out classed here...like a penguin trying to fly with eagles.

But more importantly, found I really don't need an answer now..."It is what it is"...
infinitely academic and all answers are uncertain and speculative, e.g. like the shape & size of the universe(s), what was before, and what's next billions of years from now.

But I appreciate your time, consideration, & trying to help me understand, and wish you
good speed as you & your group of fellow cosmologists wrestle with Dark Energy, Dark Matter, Quantum Gravity, strings, foam & fuzzballs.

I'll watch from afar and take more Advil.

 

[marcus]

Hi Marcus,

I've started going through this thread methodically, and am only stumbling over this
part of the BA as you describe how to visualize it mentally:
Ok, no inside or outside...is there the other side? i.e. is the curve continuous
to form a sphere? (balloons are so asymmetrical). Is the surface of the BA convex?
Would a disk would be a better analogy(?)

BTW, looked up the ΛCDM (Wiki), and that was very helpful.

Thanks for going back and reading more of the thread. I might be able to concentrate it into two or three current posts but a loose informal format has some plus sides too. Cosmology forum has a good FAQ compiled largely by Ben Crowell (prof at a college in Calif. and author of several online books if I'm not mistaken). It's my fault not yours that this thread is all spread out so that a newcomer can miss important details!

Like yes, the balloon model space is a closed edge-less 2D space. It is not like a disk. It is in all respects like the zero-thickness 2D surface of a ball or balloon EXCEPT WITHOUT THE INSIDE OR OUTSIDE 3D SPACE.

In math that is possible. You can have, and work with, and calculate with, a 2D object that does not "LIVE" in any surrounding 3D space. We say the 2D objected is not embedded in a larger 3D space. Although in some cases it COULD be embedded, but that might involve unnecessary complication.

It's not something to get a headache about, it is just people simplifying their lives by not assuming or worrying about a higher dimensional surround. Because back in 1820-1850 some guys figured out how to work within a curved space and do all the geometry and calculus they wanted without reference to points outside. It turns out that once you are equipped with the techniques, and if you have no evidence of there being an external higher dimensional space, it can be a lot simpler to just work within the given geometry and not "make up" something surrounding it.

So in that little movie of the expanding balloon surface, it really is a 2D sphere. You can probably see some photons of light going around to the other side and disappearing at your horizon, and some others coming from the other side and appearing on the horizon and moving in.

And although the balloon could obviously be embedded in a larger 3D room, and have existence inside and outside of the surface, you are encouraged to imagine it as a pure 2D thing with zero-thickness creatures and galaxies, and no inside or outside. That is encouraged because it is good practice for going mentally up one higher dimension and imagining our 3D world in an analogous way. We can't point our fingers out of it and we have no evidence of a larger surround. So we accept our limitations and don't make things up. There is no center point (in our 3D world) of the expansion. At least that is how people have over the years found it works best to think about it.

One reason it's simpler is that when uneven curvature develops, and maybe even forms an extreme case of a black hole, you don't have to worry about where it "goes"---did the black hole go inside, or outside?---no. there isn't any inside or outside, I don't have to worry. and an infinite uncurved 3D space doesn't have any inside or outside, it just has itself, so it is very much like the limit of a curved 3D space where you just let the sphere get bigger and bigger and the curvature peter out to zero. So the flat 3D case is "of a piece" with the curved 3D case, neither are embedded.

 

[megacal]

Hi Marcus,

thank you for that explanation, although it went in one neuron and out the other.
Higher math concepts are just beyond me...I think if I meditated on it long enough
it may congeal, but feeling a bit dizzy at the moment.

It is in all respects like the zero-thickness 2D surface of a ball or balloon EXCEPT WITHOUT THE INSIDE OR OUTSIDE 3D SPACE.

...do you literally mean zero thickness? Do you mean very very thin compared to the other axes?

Is the BA just a mental excercise or supposed to describe another possible model of the universe? Maybe I don't understand the object of the thread.

I'm probably hampered in that I think left-brained & most of my concentration is on 3D programs...creating fluid simulations, other worlds, and now 3D fractals. (I wonder if fractal geometry shows up in the largest structures?)

Seriously, I do appreciate your reply and will read it (and meditate on it) to see if
the fog lifts & I can say, "Aha! So that's what he meant!"

And I really did have a throbbing headache when I posted last, though not sure if
trying to grok the BA was the source.

 

[marcus]

Hi Marcus,

thank you for that explanation, although it went in one neuron and out the other.
Higher math concepts are just beyond me...I think if I meditated on it long enough
it may congeal, but feeling a bit dizzy at the moment.

...do you literally mean zero thickness? Do you mean very very thin compared to the other axes?

Is the BA just a mental excercise or supposed to describe another possible model of the universe? Maybe I don't understand the object of the thread.

I'm probably hampered in that I think left-brained & most of my concentration is on 3D programs...creating fluid simulations, other worlds, and now 3D fractals. (I wonder if fractal geometry shows up in the largest structures?)

Seriously, I do appreciate your reply and will read it (and meditate on it) to see if
the fog lifts & I can say, "Aha! So that's what he meant!"

And I really did have a throbbing headache when I posted last, though not sure if
trying to grok the BA was the source.

Take care of yourself! Avoiding throbbing headaches and enjoying the life are ultimately more important than understanding the universe. The universe does not want you to have a painful headache and it wants to be enjoyed even more than understood. It's a beautiful day here, by the way. cold air blue sky bright sunlight.

I actually meant zero thickness. A truly 2D world. And the balloon analogy (BA as you say) is really meant as an ANALOGY not a possible model of real cosmos. You can think of it as a "toy" model dumbed down from 3D (which we see) to 2D (where zero thickness amoebas live in zero thickness houses in zero thickness galaxies.)

But if thinking about that 2D expanding balloon analogy does not make you happy and relaxed you should not feel you have to!

Another avenue is to think about our own familiar 3D space as very large but curving very gently so that you could actually circumnavigate it (if you had enough time and fast enough motor scooter and it wasn't expanding). The main thing is to be able to imagine space as EDGELESS or boundaryless, and approximately evenly scattered with matter. The largescale picture looks kind of like cobweb-filled attic where the galaxies and irregular clusters of galaxies and wispy clouds of dark matter form the cobwebs that fill ALL of space.

The edgelessness and approximate on average even distribution of matter are the important things, basic to the picture that cosmologists have. They haven't seen any convincing evidence of an edge or some major largescale unevenness. So they keep it simple and don't make up stuff they haven't seen like that.

Maybe if you take a break from it and come back later it will seem natural to you. I think if it is stressful for you it could be because I have explained it the wrong way.

 

[megacal]

Maybe if you take a break from it and come back later it will seem natural to you.

...Ok...will get back asap if I have a sudden epiphany.

I think if it is stressful for you it could be because I have explained it the wrong way.

No, not at all...the failure to comprehend it is only due to my lack of background and possibly how my brain is wired. The BA just doesn't correlate with anything I can relate to...it's something I have to imagine.

But am hoping it will come into focus all of a sudden. I'm sure your explanation is perfectly
sound...it just sounds impossible. , no offense.

 

[marcus]

Jorrie calculator

Jorrie (fellow PF member) has an online cosmology calculator that embodies the standard model of the U, just as Morgan's and Ned Wright's do
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc.htm

It has some extra features and some advantages that make it easier to use, in certain respects. May also have additional precision at high redshifts. So it is definitely worth checking out.

If you want to use it and don't have the URL handy, you can (I find) get it by googling
"cosmological calculator 2010"

i know you can get Ned Wright's cosmo calculator simply by googling "Wright calculator" (or you could the last time I tried) so I am also going to try getting Jorrie's by googling: "Jorrie calculator".

It helps to have tags that are easy to remember, saves time and fumble.

 

[megacal]

Hi Marcus,

thanks for those links.

BTW, did you get my pm?